Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions

Abstract

In this paper we consider a class of (2+1)D schematic models with four-fermion interactions that are effectively used in studying condensed-matter systems with planar crystal structure, and especially graphene. Symmetry breaking in these models occurs due to a possible appearance of condensates. Special attention is paid to the symmetry properties of the appearing condensates in the framework of discrete chiral and $\mathcal{C}$, $\mathcal{P}$ and $\mathcal{T}$ transformations. Moreover, boundary conditions corresponding to carbon nanotubes are considered and their relations with the effect of an applied external magnetic field are studied. To this end we calculated the effective potential for the nanotube model including effects of finite temperature, density and an external magnetic field. As an illustration we made numerical calculations of the chiral symmetry properties in a simpler Gross--Neveu model with only one condensate taken into account. We also investigated the phase structure of the nanotube model under the influence of the Aharonov--Bohm effect and demonstrated that there is a nontrivial relation between the magnitude of the Aharonov--Bohm phase, compactification of the spatial dimension and thermal restoration of the originally broken chiral symmetry.

minor changes of the text; 37 pages, 6 figures; accepted for publication in Annals of Physics

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• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Thermodynamics of a generalized graphene-motivated (2+1)-dimensional Gross-Neveu model beyond mean field within the Beth-Uhlenbeck approach
• Variational path-integral approach to back-reactions of composite mesons in the Nambu-Jona-Lasinio model
• Magnetic Field Effect in the Fine-Structure Constant and Electron Dynamical Mass
• Superconducting phase transition in planar fermionic models with Dirac cone tilting
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model
• Four-Fermion Interaction Model on ${\mathcal{M}}^{D-1}\otimes S^1$
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• Influence of the four-fermion interactions in (2+1)D massive electrons system
• Casimir effect for fermion condensate in conical rings
• First order phase transitions within Weyl type of materials at low temperatures
• Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model
• Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$
• Beth-Uhlenbeck equation for the thermodynamics of fluctuations in a generalised 2+1D Gross-Neveu model